[1] T. A. Abrahamsen, O. Nygaard and M. P˜
oldvere, New applications of extremely regular
function spaces, Pacifc J. Math. 301 (2019), 385–394 doi:10.2140/pjm.2019.301.385
[2] J. Araujo and J. J. Font, Linear isometries between subspaces of continuous functions,
J. Araujo and J. J. Font, Trans. Amer. Math. Soc. 349 (1997), 413–428
[3] J. Araujo and J. J. Font, On Silov
boundaries for subspaces of continuous functions,
Proceedings of the First Ibero-American Conference on Topology and its Applications
(Benicassim, 1995) Topology Appl. 77 (1997), 79–85 doi:10.1016/S0166-8641(96)00132-0
[4] T. Banakh, Every 2-dimensional Banach space has the Mazur-Ulam property, Linear
Algebra Appl. 632 (2022), 268–280 doi:10.1016/j.laa.2021.09.020
[5] H. S. Bear, The Silov boundary for a linear space of continuous functions, Amer. Math.
Monthly 68 (1961), 483–485
[6] J. Becerra-Guerrero, M. Cueto-Avellaneda, F. J. Fern´
andez-Polo and A. M. Peralta, On
the extension of isometries between the unit spheres of a JBW*-triple and a Banach space,
J. Inst. Math. Jussieu 20 (2021), 277–303 doi:10.1007/s13324-022-00448-2
[7] E. Bishop and K. de Leeuw, The representation of linear functionals by measures on sets
of extreme points, Ann. Inst. Fourier, Grenoble 9 (1959), 305–331
[8] D. P. Blecher, The Shilov boundary of an operator space and the characterization theorems,
J. Funct. Anal. 182 (2001), 280–343 doi:10.1006/jfan.20003734
[9] H. F. Bohnenblust and S. Karlin, Geometrical properties of the unit sphere of Banach
algebras, Ann. Math., II. Ser. 62 (1955), 217–229
[10] K. Boyko, V. Kadets, M. Mart´ın and J. Mer´ı, Properties of lush spaces and applications to Banach spaces with numerical index 1, Studia Math. 190 (2009), 117–133
doi:10.4064/sm190-2-2
[11] K. Boyko, V. Kadets, M. Mart´ın and D. Werner,
Numerical index of Banach spaces and duality, Math. Proc. Cambridge Philos. Soc. 142 (2007), 93–102
doi:10.1017/S0305004106009650
[12] A. Browder, Introduction to function algebras, W. A. Benjamin, Inc., New YorkAmsterdam 1969 Xii+273 pp
[13] J. Cabello S´
anchez, A reflection on Tingley’s problem and some applications, J. Math.
Anal. Appl. 476 (2019), 319–336 doi:10.1016/j.jmaa.2019.03.041
[14] D. Cabezas, M. Cueto-Avellaneda, D. Hirota, T. Miura and A. Peralta, Every commutative JB*-triple satisfies the complex Mazur-Ulam property, Ann. Funct. Anal. 13 (2022),
Paper No. 60, 8pp
[15] L. Cheng and Y. Dong, On a generalized Mazur-Ulam question: extension of isometries between unit spheres of Banach spaces, J. Math. Anal. Appl. 377 (2011), 464–470
doi:10.1016/j.jmaa.2020.11.025
[16] B. Chengiz, On extremely regular function spaces, Pac. J. Math. 49 (1973), 335–338
The Mazur-Ulam property and point-separation property
81
[17] M. Cueto-Avellaneda, D. Hirota, T. Miura and A. Peralta, Exploring new solutions to
Tingley’s problem for function algebras Quaest. Math. Published online : 02 Jun 2022
[18] M. Cueto-Avellaneda and A. M. Peralta, On the Mazur-Ulam property for the space
of Hilbert-space-valued continuous functions, J. Math. Anal. Appl. 479 (2019), 875–902
doi:10.1016/j.jmaa.2019.06.056
[19] M. Cueto-Avellaneda and A. M. Peralta,
The Mazur-Ulam property for commutative von Neumann algebras, Linear Multilinear Algebra 68 (2020), 337–362
doi:10.1080/03081087.2018.1505823
[20] G. G. Ding, On extension of isometries between unit spheres of E and C(Ω), Acta Math.
Sin. (Engl. Ser.) 19 (2003), 793–800
[21] G. G. Ding, The isometric extension of the into mapping from a L∞ (Γ)-type space to
some Banach space, Illinois J. Math. 51 (2007), 445–453
[22] J. Duncan, C. McGregor, J. Pryce and A. White, The numerical index of a normed space,
J. London Math. Soc. 2 (1970), 481–488
[23] X. N. Fang and J. H. Wang, Extension of isometries between the unit spheres of normed
space and C(Ω), Acta Math.Sinica Engl Ser. 22 (2006), 1819–1824
[24] R. J. Fleming and J. E. Jamison, Isometries on Banach spaces: function spaces, Chapman
& Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, 129. Chapman
& Hall/CRC, Boca Raton, FL, 2003. x+197 pp. ISBN: 1-58488-040-6
[25] T. W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1969
[26] O. Hatori, The Mazur-Ulam property for uniform algebras, Studia Math. 265 (2022),
227–239 doi: 10.4064/sm210703-11-9
[27] O. Hatori, S. Oi and R. Shindo Togashi, Tingley’s problems on uniform algebras Jour.
Math. Anal. Appl. 503 (2021), Paper No. 125346, 14 pp. doi: 10.1016/j.jmaa.2021.125346
[28] A. Jim´enez-Vargas, A. Morales-Campoy, A. M. Peralta and M. I. Ram´ırez, The MazurUlam property for the space of complex null sequences, Linear Multilinear Algebra 67
(2019), 799–816 doi:10.1080/03081087.2018.1433625
[29] V. M. Kadets and M. M. Popov, The Daugavet property for narrow operators in rich
subspaces of C[0, 1] and L1 [0, 1], St. Petersburg Math. J. 8 (1997), 571–584
boundary, Math. Z. 202
[30] P. Kajetanowicz, A general approach to the notion of Silov
(1989), 391–395
[31] O. F. K. Kalenda and A. M. Peralta, Extension of isometries from the unit sphere of a
rank-2 Cartan factor, Anal. Math. Phys. 11, Article number:15 (2021)
[32] R. Liu, On extension of isometries between unit spheres of L∞ (Γ)-type space and a Banach
space E, J. Math. Anal. Appl. 333 (2007), 959–970 doi:10.1016/j.jmaa.2006.11.044
[33] T. Miura, Real-linear isometries between function algebras, Cent. Eur. J. Math. 9 (2011),
778–788 doi:10.2478/s11533-011-0044-9
[34] M. Mori, Tingley’s problem through the facial structure of operator algebras, J. Math.
Anal. Appl. 466 (2018), 1281–1298 doi:10.1016/j.jmaa.2018.06.050
[35] M. Mori and N. Ozawa, Mankiewicz’s theorem and the Mazur-Ulam property for C ∗ algebras, Studia Math. 250 (2020), 265–281 doi:10.4064/sm180727-14-11
[36] W. Novinger, Linear isometries of subspaces of continuous functions, Studia Math. 53
(1975), 273–276
[37] R. R. Phelps, Lectures on Choquet’s Theorem. Second edition, Lecture Notes in Mathematics, 1757. Springer-Verlag, Berlin, 2001
[38] A. M. Peralta, Extending surjective isometries defined on the unit sphere of ℓ∞ (Γ) Rev.
Mat. Complut. 32 (2019), 99–114 doi:10.1007/s13163-018-0269-2
82
Osamu Hatori
[39] A. M. Peralta, On the extension of surjective isometries whose domain is the unit sphere
of a space of compact operators, Filmat 36 (2022), 3075–3090
[40] A. Peralta and R. Svarc,
A strengthened Kadison’s transitivity theorem for unital JB*algebras with applications to the Mazur-Ulam property, preprint 2023, arXiv:2301.00895
[41] Ch. Pomerenke, Boundary behavior of conformal maps, Grundlehrender Mathematischen
Wissenschaften, 299 Springer-Verlag, Berlin, 1992, x+300 pp
[42] N. V. Rao and A. K. Rao, Multiplicatively spectrum-preserving maps of function algebras.
II, Proc. Edinb. Math. Soc. 48 (2005), 219–229
[43] T. S. S. R. K. Rao and A. K. Roy, On Silov
boundary for function spaces, Topology Appl.
193 (2015), 175–181 doi:10.1016/j.topol.2015.07.005
[44] Z. Semadeni,
Banach spaces of continuous functions, Monografie Matematyczne,
Warszawa, 1971
[45] G. Silov,
On the extension of maximal ideals, Dokl. Akad. Nauk SSSR 29 (1940), 83–84
(in Russian)
[46] E. L. Stout, The theory of uniform algebras, Bogden & Quigley, Inc. Publishers,
Tarrytown-on-Hudson, N. Y., 1971
[47] D. N. Tan, Extension of isometries on unit spheres of L∞ , Taiwanese J. Math. 15 (2011),
819–827
[48] D. N. Tan, On extension of isometries on the unit spheres of Lp -spaces for 0 < p ≤ 1,
Nonlinear Anal. 74 (2011), 6981–6987 doi:10.1016/j.na.2011.07.035
[49] D. N. Tan, Extension of isometries on the unit sphere of Lp spaces, Acta Math. Sin.
(Engl. Ser.) 28 (2012), 1197–1208 doi:10.1007/s10114-011-0302-6
[50] D. Tan, X. Huang and R. Liu, Generalized-lush spaces and the Mazur-Ulam property,
Studia Math. 219 (2013), 139–153 doi:10.4064/sm219-2-4
[51] R. Tanaka, A further property of spherical isometries, Bull. Aust. Math. Soc. 90 (2014),
304–310 doi:10.1017/S0004972714000185
[52] R. Tanaka, The solution of Tingley’s problem for the operator norm unit sphere of complex
n × n matrices, Linear Algebra Appl. 494 (2016), 274–285 doi:10.1016/j.laa.2016.01.020
[53] D. Tingley, Isometries of the unit sphere, Geom. Dedicata 22 (1987), 371–378
[54] R. S. Wang, Isometries between the unit spheres of C0 (Ω) type spaces, Acta Math. Sci.
(English Ed.) 14 (1994), 82–89
(n)
[55] Risheng Wang, Isometries of C0 (X), Hokkaido Math. J. 25 (1996), 465–519
doi:10.14492/hokmj/1351516747
[56] Ruidong Wang and X. Huang, The Mazur-Ulam property for two dimensional somewhereflat spaces, Linear Algebra Appl. 562 (2019), 55–62 doi:10.1016/j.laa.2018.09.024
[57] P. Wojtaszczyk, Some remarks on the Daugavet equation, Proc. Amer. Math. Soc. 115
(1992), 1047–1052
[58] X. Yang and X. Zhao, On the extension problems of isometric and nonexpansive mappings,
In:Mathematics without boundaries. Edited by Themistocles M. Rassias and Panos M.
Pardalos, 725– Springer, New York, 2014
...